mirror of
https://github.com/storytold/wordcraft.git
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1001 lines
34 KiB
Rust
1001 lines
34 KiB
Rust
//! Equations: the Office Math object model (OMML, ECMA-376 Part 1 §22.1) as a tree, its linear
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//! format (UnicodeMath, the plain text Word shows for an equation) and a parser for that format.
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//!
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//! An equation is a list of [`MNode`]s (an *argument*); structures hold arguments of their own
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//! (a fraction's numerator and denominator, a radical's degree and base…). Layout reads the tree;
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//! DOCX import builds it from OMML and keeps the source XML so a saved file carries the equation
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//! exactly as Word wrote it.
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use serde::{Deserialize, Serialize};
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use crate::props::Rgb;
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/// A sequence of math nodes (OMML's `m:e`, `m:num`, `m:sub`…).
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pub type Arg = Vec<MNode>;
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/// Deepest structure nesting kept (parsers stop here; layout draws nothing deeper).
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pub const MAX_DEPTH: usize = 64;
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/// An equation's structure, plus what's needed to write it back.
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#[derive(Clone, Debug, PartialEq, Default, Serialize, Deserialize)]
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pub struct Math {
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#[serde(default, skip_serializing_if = "Vec::is_empty")]
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pub nodes: Arg,
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/// The source `m:oMath` element (DOCX import), written back unchanged on save. Empty for
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/// equations made here.
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#[serde(default, skip_serializing_if = "String::is_empty")]
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pub omml: String,
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/// Justification of a display equation.
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#[serde(default, skip_serializing_if = "is_default")]
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pub jc: MathJc,
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/// Shown as its linear-format text (Equation › Convert › Linear) instead of built up.
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#[serde(default, skip_serializing_if = "is_default")]
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pub linear: bool,
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}
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fn is_default<T: Default + PartialEq>(v: &T) -> bool {
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*v == T::default()
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}
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impl Math {
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pub fn is_empty(&self) -> bool {
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self.nodes.is_empty()
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}
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}
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/// Display equation justification (`m:oMathParaPr/m:jc`).
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Default, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum MathJc {
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#[default]
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CenterGroup,
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Center,
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Left,
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Right,
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}
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/// Where a display equation too wide for its line breaks at a binary operator (`m:brkBin`).
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Default, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum BrkBin {
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/// The operator starts the next line.
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#[default]
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Before,
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/// The operator ends the line.
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After,
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/// The operator ends the line and starts the next one again.
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Repeat,
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}
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/// How a minus repeats across a break when [`BrkBin::Repeat`] (`m:brkBinSub`): the operator
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/// ending the line, then the one starting the next.
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Default, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum BrkBinSub {
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/// `--`
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#[default]
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MinusMinus,
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/// `-+`
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MinusPlus,
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/// `+-`
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PlusMinus,
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}
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/// Document-wide equation options (`m:mathPr` in the settings part) that layout uses: how long
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/// display equations wrap.
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#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
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#[serde(default, rename_all = "camelCase")]
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pub struct MathProps {
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pub brk_bin: BrkBin,
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pub brk_bin_sub: BrkBinSub,
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/// Indent of a wrapped equation's continuation lines, points (`m:wrapIndent`).
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pub wrap_indent: f32,
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/// Continuation lines align right instead (`m:wrapRight`).
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pub wrap_right: bool,
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}
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/// `m:wrapIndent`'s default: 1440 twips, one inch.
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pub const DEFAULT_WRAP_INDENT: f32 = 72.0;
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impl Default for MathProps {
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fn default() -> Self {
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MathProps { brk_bin: BrkBin::Before, brk_bin_sub: BrkBinSub::MinusMinus, wrap_indent: DEFAULT_WRAP_INDENT, wrap_right: false }
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}
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}
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/// Math run style (`m:sty`): plain, bold, italic, bold italic.
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum MSty {
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Plain,
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Bold,
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Italic,
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BoldItalic,
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}
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/// Math alphabet (`m:scr`).
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Default, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum MScr {
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#[default]
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Roman,
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Script,
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Fraktur,
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DoubleStruck,
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SansSerif,
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Monospace,
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}
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/// A run of math text (`m:r`).
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#[derive(Clone, Debug, PartialEq, Default, Serialize, Deserialize)]
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pub struct MRun {
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pub text: String,
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/// `None`: math default (letters italic, the rest upright).
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#[serde(default, skip_serializing_if = "Option::is_none")]
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pub sty: Option<MSty>,
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#[serde(default, skip_serializing_if = "is_default")]
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pub scr: MScr,
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/// Normal (non-math) text.
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#[serde(default, skip_serializing_if = "is_default")]
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pub nor: bool,
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/// Literal: no automatic operator handling.
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#[serde(default, skip_serializing_if = "is_default")]
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pub lit: bool,
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/// Font size, points.
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#[serde(default, skip_serializing_if = "Option::is_none")]
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pub size: Option<f32>,
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#[serde(default, skip_serializing_if = "Option::is_none")]
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pub color: Option<Rgb>,
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/// Font for normal text.
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#[serde(default, skip_serializing_if = "Option::is_none")]
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pub font: Option<String>,
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/// A manual line break before this run in a display equation (`m:brk`): `Some(0)` wraps as
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/// usual, `Some(n)` aligns the new line at the `n`th operator of the first line (`m:alnAt`).
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#[serde(default, skip_serializing_if = "Option::is_none")]
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pub brk: Option<u8>,
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}
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impl MRun {
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pub fn new(text: impl Into<String>) -> MRun {
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MRun { text: text.into(), ..Default::default() }
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}
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pub fn plain(text: impl Into<String>) -> MRun {
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MRun { text: text.into(), sty: Some(MSty::Plain), ..Default::default() }
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}
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}
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Default, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum FracKind {
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/// Stacked with a rule.
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#[default]
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Bar,
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/// Skewed (num ⁄ den).
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Skewed,
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/// Linear (num/den).
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Linear,
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/// Stacked without a rule.
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NoBar,
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}
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum ScriptKind {
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Sup,
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Sub,
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SubSup,
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/// Pre-scripts (`m:sPre`).
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Pre,
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}
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/// Where an n-ary operator's limits go.
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum LimLoc {
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/// Under and over the operator.
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UndOvr,
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/// As sub- and superscripts.
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SubSup,
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}
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/// Column justification in a matrix.
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#[derive(Clone, Copy, Debug, PartialEq, Eq, Default, Serialize, Deserialize)]
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#[serde(rename_all = "camelCase")]
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pub enum ColJc {
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#[default]
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Center,
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Left,
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Right,
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}
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/// A math node.
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#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
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#[serde(tag = "t", rename_all = "camelCase")]
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pub enum MNode {
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Run(MRun),
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/// `m:f`.
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Frac {
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#[serde(default)]
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kind: FracKind,
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num: Arg,
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den: Arg,
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},
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/// `m:sSup`, `m:sSub`, `m:sSubSup`, `m:sPre`.
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Script {
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kind: ScriptKind,
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base: Arg,
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#[serde(default)]
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sub: Arg,
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#[serde(default)]
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sup: Arg,
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},
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/// `m:rad`.
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Rad {
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#[serde(default)]
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deg: Arg,
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#[serde(default)]
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deg_hide: bool,
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e: Arg,
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},
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/// `m:nary`: ∑ ∫ ∏ … with limits and an operand.
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Nary {
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chr: char,
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/// `None`: Word's default (integrals take sub/sup limits, the rest under/over).
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#[serde(default)]
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lim_loc: Option<LimLoc>,
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#[serde(default)]
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grow: bool,
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#[serde(default)]
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sub_hide: bool,
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#[serde(default)]
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sup_hide: bool,
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#[serde(default)]
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sub: Arg,
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#[serde(default)]
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sup: Arg,
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e: Arg,
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},
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/// `m:d`: delimiters around elements separated by `sep`.
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Delim {
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/// `None` = no delimiter.
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beg: Option<char>,
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end: Option<char>,
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#[serde(default)]
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sep: Option<char>,
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/// Delimiters grow to the content (Word's default).
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#[serde(default = "yes")]
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grow: bool,
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/// Grow to match the content exactly rather than centred on the math axis.
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#[serde(default)]
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shp_match: bool,
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elems: Vec<Arg>,
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},
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/// `m:func`: function name applied to an argument (sin x).
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Func {
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name: Arg,
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e: Arg,
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},
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/// `m:limLow` / `m:limUpp`.
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Lim {
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upper: bool,
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e: Arg,
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lim: Arg,
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},
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/// `m:acc`: accent over the base.
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Acc {
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chr: char,
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e: Arg,
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},
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/// `m:bar`: overbar or underbar.
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Bar {
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top: bool,
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e: Arg,
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},
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/// `m:borderBox`. `hide`: top, bottom, left, right. `strike`: horizontal, vertical,
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/// bottom-left→top-right, top-left→bottom-right.
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BorderBox {
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#[serde(default)]
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hide: [bool; 4],
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#[serde(default)]
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strike: [bool; 4],
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e: Arg,
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},
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/// `m:box`.
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Boxed {
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e: Arg,
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},
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/// `m:groupChr`: a stretched character (brace, arrow) under or over the base.
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GroupChr {
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chr: char,
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top: bool,
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e: Arg,
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},
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/// `m:eqArr`: rows aligned at `&`.
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EqArr {
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rows: Vec<Arg>,
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},
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/// `m:m`.
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Matrix {
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rows: Vec<Vec<Arg>>,
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#[serde(default)]
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col_jc: Vec<ColJc>,
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},
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/// `m:phant`.
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Phant {
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#[serde(default = "yes")]
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show: bool,
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#[serde(default)]
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zero_wid: bool,
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#[serde(default)]
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zero_asc: bool,
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#[serde(default)]
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zero_desc: bool,
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e: Arg,
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},
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}
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fn yes() -> bool {
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true
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}
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/// A row holds an equation-number mark (`#`) in a top-level run.
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pub fn has_number_mark(row: &[MNode]) -> bool {
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row.iter().any(|n| matches!(n, MNode::Run(r) if !r.lit && !r.nor && r.text.contains('#')))
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}
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/// Integral signs (their limits default to sub/sup positions).
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pub fn is_integral(c: char) -> bool {
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matches!(c, '∫' | '∬' | '∭' | '∮' | '∯' | '∰' | '∱' | '∲' | '∳' | '⨌')
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}
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/// Characters that take n-ary operator form in the linear format.
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pub fn is_nary_char(c: char) -> bool {
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is_integral(c) || matches!(c, '∑' | '∏' | '∐' | '⋃' | '⋂' | '⋁' | '⋀' | '⨁' | '⨂' | '⨀' | '⨄' | '⨆')
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}
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/// Mathematical alphanumeric for `c` in a style and alphabet (Unicode block U+1D400).
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pub fn math_alnum(c: char, bold: bool, italic: bool, scr: MScr) -> char {
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let off = |base: u32, k: u32| char::from_u32(base + k).unwrap_or(c);
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let upper = c.is_ascii_uppercase();
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let lower = c.is_ascii_lowercase();
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if upper || lower {
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let k = if upper { c as u32 - 'A' as u32 } else { c as u32 - 'a' as u32 };
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// Letters that live in the Letterlike Symbols block.
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let hole = |table: &[(char, char)]| table.iter().find(|(f, _)| *f == c).map(|(_, t)| *t);
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let (base_u, base_l) = match (scr, bold, italic) {
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(MScr::Roman, false, false) => return c,
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(MScr::Roman, true, false) => (0x1D400, 0x1D41A),
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(MScr::Roman, false, true) => {
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if c == 'h' {
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return '\u{210E}';
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}
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(0x1D434, 0x1D44E)
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}
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(MScr::Roman, true, true) => (0x1D468, 0x1D482),
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(MScr::Script, false, _) => {
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if let Some(t) = hole(&[
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('B', 'ℬ'),
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('E', 'ℰ'),
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('F', 'ℱ'),
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('H', 'ℋ'),
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('I', 'ℐ'),
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('L', 'ℒ'),
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('M', 'ℳ'),
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('R', 'ℛ'),
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('e', 'ℯ'),
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('g', 'ℊ'),
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('o', 'ℴ'),
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]) {
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return t;
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}
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(0x1D49C, 0x1D4B6)
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}
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(MScr::Script, true, _) => (0x1D4D0, 0x1D4EA),
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(MScr::Fraktur, false, _) => {
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if let Some(t) = hole(&[('C', 'ℭ'), ('H', 'ℌ'), ('I', 'ℑ'), ('R', 'ℜ'), ('Z', 'ℨ')]) {
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return t;
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}
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(0x1D504, 0x1D51E)
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}
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(MScr::Fraktur, true, _) => (0x1D56C, 0x1D586),
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(MScr::DoubleStruck, _, _) => {
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if let Some(t) = hole(&[('C', 'ℂ'), ('H', 'ℍ'), ('N', 'ℕ'), ('P', 'ℙ'), ('Q', 'ℚ'), ('R', 'ℝ'), ('Z', 'ℤ')]) {
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return t;
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}
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(0x1D538, 0x1D552)
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}
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(MScr::SansSerif, false, false) => (0x1D5A0, 0x1D5BA),
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(MScr::SansSerif, true, false) => (0x1D5D4, 0x1D5EE),
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(MScr::SansSerif, false, true) => (0x1D608, 0x1D622),
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(MScr::SansSerif, true, true) => (0x1D63C, 0x1D656),
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(MScr::Monospace, _, _) => (0x1D670, 0x1D68A),
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};
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return off(if upper { base_u } else { base_l }, k);
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}
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if c.is_ascii_digit() {
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let k = c as u32 - '0' as u32;
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return match (scr, bold) {
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(MScr::Roman, true) => off(0x1D7CE, k),
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(MScr::DoubleStruck, _) => off(0x1D7D8, k),
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(MScr::SansSerif, false) => off(0x1D7E2, k),
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(MScr::SansSerif, true) => off(0x1D7EC, k),
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(MScr::Monospace, _) => off(0x1D7F6, k),
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_ => c,
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};
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}
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// Greek (roman alphabet only).
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if scr == MScr::Roman && (bold || italic) {
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let (cap, small) = match (bold, italic) {
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(true, false) => (0x1D6A8, 0x1D6C2),
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(false, true) => (0x1D6E2, 0x1D6FC),
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_ => (0x1D71C, 0x1D736),
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};
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let u = c as u32;
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if (0x391..=0x3A9).contains(&u) && u != 0x3A2 {
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return off(cap, u - 0x391);
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}
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if (0x3B1..=0x3C9).contains(&u) {
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return off(small, u - 0x3B1);
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}
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let extra = match c {
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'∂' => Some(25),
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'ϵ' => Some(26),
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'ϑ' => Some(27),
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'ϰ' => Some(28),
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'ϕ' => Some(29),
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'ϱ' => Some(30),
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'ϖ' => Some(31),
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_ => None,
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};
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if let Some(e) = extra
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&& italic
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{
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return off(small, e);
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}
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}
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c
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}
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// ---------------------------------------------------------------------------------------------
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// Linear format out.
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/// The equation as linear-format text (`x=(-b±√(b^2-4ac))/2a`).
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pub fn to_linear(nodes: &[MNode]) -> String {
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let mut s = String::new();
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lin_arg(nodes, &mut s, 0);
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s
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}
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fn lin_arg(a: &[MNode], s: &mut String, depth: usize) {
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if depth > MAX_DEPTH {
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return;
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}
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for n in a {
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lin_node(n, s, depth + 1);
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}
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}
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||
|
||
/// An argument as an operand: bare when it's a single simple atom, parenthesised otherwise.
|
||
fn lin_operand(a: &[MNode], s: &mut String, depth: usize) {
|
||
let mut inner = String::new();
|
||
lin_arg(a, &mut inner, depth);
|
||
let simple = match a {
|
||
[MNode::Run(r)] => {
|
||
let mut cs = r.text.chars();
|
||
match (cs.next(), cs.next()) {
|
||
(Some(c), None) => !"+-−=/^_ ".contains(c),
|
||
_ => r.text.chars().all(|c| c.is_alphanumeric() || c == '.'),
|
||
}
|
||
}
|
||
[MNode::Delim { .. }] => true,
|
||
_ => false,
|
||
};
|
||
if simple && !inner.is_empty() {
|
||
s.push_str(&inner);
|
||
} else {
|
||
s.push('(');
|
||
s.push_str(&inner);
|
||
s.push(')');
|
||
}
|
||
}
|
||
|
||
/// A script or limit operand. The parser reads a script as one letter or a number (`x_10`), so a
|
||
/// longer run is grouped: `V_(dd)`, not `V_dd` (which reads back as V_d then d).
|
||
fn lin_script(a: &[MNode], s: &mut String, depth: usize) {
|
||
if let [MNode::Run(r)] = a
|
||
&& r.text.chars().nth(1).is_some()
|
||
&& !(r.text.starts_with(|c: char| c.is_ascii_digit()) && r.text.chars().all(|c| c.is_ascii_digit() || c == '.'))
|
||
{
|
||
s.push('(');
|
||
s.push_str(&r.text);
|
||
s.push(')');
|
||
} else {
|
||
lin_operand(a, s, depth);
|
||
}
|
||
}
|
||
|
||
fn lin_node(n: &MNode, s: &mut String, depth: usize) {
|
||
match n {
|
||
MNode::Run(r) => s.push_str(&r.text),
|
||
MNode::Frac { kind, num, den } => {
|
||
lin_operand(num, s, depth);
|
||
s.push(match kind {
|
||
FracKind::Skewed => '⁄',
|
||
FracKind::Linear => '∕',
|
||
FracKind::NoBar => '¦',
|
||
FracKind::Bar => '/',
|
||
});
|
||
lin_operand(den, s, depth);
|
||
}
|
||
MNode::Script { kind, base, sub, sup } => {
|
||
if *kind == ScriptKind::Pre {
|
||
s.push('_');
|
||
lin_script(sub, s, depth);
|
||
s.push('^');
|
||
lin_script(sup, s, depth);
|
||
s.push('▒');
|
||
lin_operand(base, s, depth);
|
||
return;
|
||
}
|
||
lin_operand(base, s, depth);
|
||
if matches!(kind, ScriptKind::Sub | ScriptKind::SubSup) {
|
||
s.push('_');
|
||
lin_script(sub, s, depth);
|
||
}
|
||
if matches!(kind, ScriptKind::Sup | ScriptKind::SubSup) {
|
||
s.push('^');
|
||
lin_script(sup, s, depth);
|
||
}
|
||
}
|
||
MNode::Rad { deg, deg_hide, e } => {
|
||
if *deg_hide || deg.is_empty() {
|
||
s.push('√');
|
||
lin_operand(e, s, depth);
|
||
} else {
|
||
s.push_str("√(");
|
||
lin_arg(deg, s, depth);
|
||
s.push('&');
|
||
lin_arg(e, s, depth);
|
||
s.push(')');
|
||
}
|
||
}
|
||
MNode::Nary { chr, sub_hide, sup_hide, sub, sup, e, .. } => {
|
||
s.push(*chr);
|
||
if !sub_hide && !sub.is_empty() {
|
||
s.push('_');
|
||
lin_script(sub, s, depth);
|
||
}
|
||
if !sup_hide && !sup.is_empty() {
|
||
s.push('^');
|
||
lin_script(sup, s, depth);
|
||
}
|
||
s.push('▒');
|
||
lin_operand(e, s, depth);
|
||
}
|
||
MNode::Delim { beg, end, elems, .. } => {
|
||
// A standard pair writes as itself; anything else uses explicit `├X … Y┤`.
|
||
let pair = matches!((beg, end), (Some(b), Some(e)) if crate::math_linear::closer(*b) == Some(*e));
|
||
let invisible = beg.is_none() && end.is_none();
|
||
if pair {
|
||
s.extend(*beg);
|
||
} else if invisible {
|
||
s.push('〖');
|
||
} else {
|
||
s.push('├');
|
||
s.extend(*beg);
|
||
}
|
||
for (i, e) in elems.iter().enumerate() {
|
||
if i > 0 {
|
||
s.push('│');
|
||
}
|
||
lin_arg(e, s, depth);
|
||
}
|
||
if pair {
|
||
s.extend(*end);
|
||
} else if invisible {
|
||
s.push('〗');
|
||
} else {
|
||
s.extend(*end);
|
||
s.push('┤');
|
||
}
|
||
}
|
||
MNode::Func { name, e } => {
|
||
lin_arg(name, s, depth);
|
||
s.push('\u{2061}');
|
||
lin_operand(e, s, depth);
|
||
}
|
||
MNode::Lim { upper, e, lim } => {
|
||
lin_operand(e, s, depth);
|
||
s.push(if *upper { '┴' } else { '┬' });
|
||
lin_script(lim, s, depth);
|
||
}
|
||
MNode::Acc { chr, e } => {
|
||
lin_operand(e, s, depth);
|
||
s.push(*chr);
|
||
}
|
||
MNode::Bar { top, e } => {
|
||
s.push(if *top { '¯' } else { '▁' });
|
||
lin_operand(e, s, depth);
|
||
}
|
||
MNode::BorderBox { e, .. } => {
|
||
s.push('▭');
|
||
lin_operand(e, s, depth);
|
||
}
|
||
MNode::Boxed { e } => {
|
||
s.push('□');
|
||
lin_operand(e, s, depth);
|
||
}
|
||
MNode::GroupChr { chr, e, .. } => {
|
||
s.push(*chr);
|
||
lin_operand(e, s, depth);
|
||
}
|
||
// A numbered equation (`E=mc^2#(1)`) is written as its one row.
|
||
MNode::EqArr { rows } if rows.len() == 1 && rows.first().is_some_and(|r| has_number_mark(r)) => {
|
||
if let Some(r) = rows.first() {
|
||
lin_arg(r, s, depth);
|
||
}
|
||
}
|
||
MNode::EqArr { rows } => {
|
||
s.push_str("█(");
|
||
for (i, r) in rows.iter().enumerate() {
|
||
if i > 0 {
|
||
s.push('@');
|
||
}
|
||
lin_arg(r, s, depth);
|
||
}
|
||
s.push(')');
|
||
}
|
||
MNode::Matrix { rows, .. } => {
|
||
s.push_str("■(");
|
||
for (i, r) in rows.iter().enumerate() {
|
||
if i > 0 {
|
||
s.push('@');
|
||
}
|
||
for (j, c) in r.iter().enumerate() {
|
||
if j > 0 {
|
||
s.push('&');
|
||
}
|
||
lin_arg(c, s, depth);
|
||
}
|
||
}
|
||
s.push(')');
|
||
}
|
||
MNode::Phant { e, .. } => {
|
||
s.push('⟡');
|
||
lin_operand(e, s, depth);
|
||
}
|
||
}
|
||
}
|
||
|
||
// ---------------------------------------------------------------------------------------------
|
||
// Linear format in.
|
||
|
||
/// Parse linear-format text into nodes ([`crate::math_linear`]). Never fails: what isn't
|
||
/// understood stays as text.
|
||
pub fn parse_linear(s: &str) -> Arg {
|
||
crate::math_linear::parse(s)
|
||
}
|
||
|
||
pub use crate::math_linear::FUNCTION_NAMES;
|
||
|
||
/// Spacing class of a math character (TeX's atom classes).
|
||
#[derive(Clone, Copy, Debug, PartialEq, Eq, Default)]
|
||
pub enum MClass {
|
||
#[default]
|
||
Ord,
|
||
Op,
|
||
Bin,
|
||
Rel,
|
||
Open,
|
||
Close,
|
||
Punct,
|
||
Inner,
|
||
}
|
||
|
||
/// The spacing class of a character in an equation.
|
||
pub fn math_class(c: char) -> MClass {
|
||
match c {
|
||
'+' | '−' | '-' | '±' | '∓' | '×' | '÷' | '·' | '∙' | '∗' | '*' | '∘' | '⊕' | '⊖' | '⊗' | '⊘' | '⊙' | '⊚' | '⊛' | '∪' | '∩' | '∧' | '∨'
|
||
| '∖' | '⋅' | '⋆' | '⊎' | '⊓' | '⊔' | '⋄' | '⊞' | '⊟' | '⊠' | '⊡' | '⋉' | '⋊' | '⋋' | '⋌' | '⋎' | '⋏' | '⋒' | '⋓' | '∔' | '∸' | '≀' | '⨿'
|
||
| '⊼' | '⊻' | '⊽' => MClass::Bin,
|
||
'=' | '<' | '>' | '≤' | '≥' | '≠' | '≈' | '≡' | '≢' | '∼' | '≃' | '≅' | '≐' | '∝' | '≪' | '≫' | '≺' | '≻' | '≼' | '≽' | '⊂' | '⊃' | '⊆'
|
||
| '⊇' | '⊄' | '⊅' | '⊈' | '⊉' | '⊊' | '⊋' | '∈' | '∉' | '∋' | '∌' | '⊥' | '∥' | '∦' | '∣' | '∤' | '≔' | '≕' | '≝' | '≜' | '≞' | '≟' | '→'
|
||
| '←' | '↔' | '⇒' | '⇐' | '⇔' | '↦' | '⟼' | '⟶' | '⟵' | '⟷' | '⟹' | '⟸' | '⟺' | '↑' | '↓' | '↕' | '⇑' | '⇓' | '⇕' | '↗' | '↘' | '↙' | '↖'
|
||
| '⊢' | '⊣' | '⊨' | '⊩' | '⊪' | '⊬' | '⊭' | '⊮' | '⊯' | '≲' | '≳' | '≍' | '⊏' | '⊐' | '⊑' | '⊒' | '⋢' | '⋣' | '≶' | '≷' | '≮' | '≯' | '≰'
|
||
| '≱' | '≦' | '≧' | '⩽' | '⩾' | ':' | '∶' | '∷' | '∺' | '∻' | '≗' | '≙' | '≚' | '≑' | '≒' | '≓' | '≖' | '⇌' | '⇋' | '⇄' | '⇆' | '⇇' | '⇉'
|
||
| '⇈' | '⇊' | '↪' | '↩' | '↼' | '↽' | '⇀' | '⇁' | '↿' | '↾' | '⇃' | '⇂' | '↶' | '↷' | '↺' | '↻' | '⊸' | '↜' | '↝' | '↞' | '↠' | '↢' | '↣'
|
||
| '↫' | '↬' | '↭' | '⇚' | '⇛' | '↰' | '↱' | '⇝' | '≁' | '≄' | '≉' | '≇' | '≭' | '≨' | '≩' | '⊀' | '⊁' | '⋠' | '⋡' | '⋦' | '⋧' | '⋨' | '⋩'
|
||
| '⋪' | '⋫' | '⋬' | '⋭' | '⋈' | '∴' | '∵' | '≏' | '≎' | '⋘' | '⋙' | '⊲' | '⊳' | '⊴' | '⊵' | '⋐' | '⋑' => {
|
||
MClass::Rel
|
||
}
|
||
'(' | '[' | '{' | '⟨' | '⌈' | '⌊' | '⟦' | '〈' => MClass::Open,
|
||
')' | ']' | '}' | '⟩' | '⌉' | '⌋' | '⟧' | '〉' | '!' => MClass::Close,
|
||
',' | ';' => MClass::Punct,
|
||
c if is_nary_char(c) => MClass::Op,
|
||
_ => MClass::Ord,
|
||
}
|
||
}
|
||
|
||
/// Merge adjacent runs with the same formatting; recurse into every structure.
|
||
pub fn merge_runs(a: Arg) -> Arg {
|
||
let mut out: Arg = Vec::with_capacity(a.len());
|
||
for n in a {
|
||
let n = match n {
|
||
MNode::Run(r) => {
|
||
if let Some(MNode::Run(prev)) = out.last_mut()
|
||
&& prev.sty == r.sty
|
||
&& prev.scr == r.scr
|
||
&& prev.nor == r.nor
|
||
&& prev.lit == r.lit
|
||
&& prev.size == r.size
|
||
&& prev.color == r.color
|
||
&& prev.font == r.font
|
||
&& r.brk.is_none()
|
||
{
|
||
prev.text.push_str(&r.text);
|
||
continue;
|
||
}
|
||
MNode::Run(r)
|
||
}
|
||
other => crate::math_linear::map_args(other, &merge_runs),
|
||
};
|
||
out.push(n);
|
||
}
|
||
out
|
||
}
|
||
|
||
/// Deepest node (a leaf counts 1) the parsers wrap further. Half of [`MAX_DEPTH`]: serde_json
|
||
/// stops reading at 128 nested containers and a node costs two (object and array).
|
||
pub(crate) const WRAP_DEPTH: usize = MAX_DEPTH / 2;
|
||
|
||
/// Calls `f` with every argument of `n`.
|
||
fn each_arg<'a>(n: &'a MNode, f: &mut impl FnMut(&'a [MNode])) {
|
||
match n {
|
||
MNode::Run(_) => {}
|
||
MNode::Frac { num, den, .. } => {
|
||
f(num);
|
||
f(den);
|
||
}
|
||
MNode::Script { base, sub, sup, .. } => {
|
||
f(base);
|
||
f(sub);
|
||
f(sup);
|
||
}
|
||
MNode::Rad { deg, e, .. } => {
|
||
f(deg);
|
||
f(e);
|
||
}
|
||
MNode::Nary { sub, sup, e, .. } => {
|
||
f(sub);
|
||
f(sup);
|
||
f(e);
|
||
}
|
||
MNode::Delim { elems, .. } => elems.iter().for_each(|a| f(a)),
|
||
MNode::Func { name, e } => {
|
||
f(name);
|
||
f(e);
|
||
}
|
||
MNode::Lim { e, lim, .. } => {
|
||
f(e);
|
||
f(lim);
|
||
}
|
||
MNode::Acc { e, .. }
|
||
| MNode::Bar { e, .. }
|
||
| MNode::BorderBox { e, .. }
|
||
| MNode::Boxed { e }
|
||
| MNode::GroupChr { e, .. }
|
||
| MNode::Phant { e, .. } => f(e),
|
||
MNode::EqArr { rows } => rows.iter().for_each(|a| f(a)),
|
||
MNode::Matrix { rows, .. } => rows.iter().flatten().for_each(|a| f(a)),
|
||
}
|
||
}
|
||
|
||
/// `n` is already nested too deeply to be wrapped in another structure. The parsers use this so
|
||
/// `x^1^1^1…` stays shallow (a left-nested tree 10 000 deep overflows the stack in `Clone`,
|
||
/// `Drop`, `PartialEq` and serde). Iterative, stops at the first too-deep path; costs at most the
|
||
/// size of `n`, which the parsers' input caps bound.
|
||
pub(crate) fn too_deep(n: &MNode) -> bool {
|
||
let mut stack: Vec<(&MNode, usize)> = vec![(n, 1)];
|
||
while let Some((n, d)) = stack.pop() {
|
||
if d >= WRAP_DEPTH {
|
||
return true;
|
||
}
|
||
each_arg(n, &mut |a| stack.extend(a.iter().map(|c| (c, d + 1))));
|
||
}
|
||
false
|
||
}
|
||
|
||
/// Any of `a` is too deep to be wrapped ([`too_deep`]).
|
||
pub(crate) fn any_too_deep(a: &[MNode]) -> bool {
|
||
a.iter().any(too_deep)
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
use super::*;
|
||
|
||
fn run(t: &str) -> MNode {
|
||
MNode::Run(MRun::new(t))
|
||
}
|
||
|
||
#[test]
|
||
fn quadratic_formula_parses_into_structures() {
|
||
let n = parse_linear("x=(-b±√(b^2-4ac))/2a");
|
||
assert_eq!(n.len(), 2, "{n:#?}");
|
||
assert_eq!(n[0], run("x="));
|
||
let MNode::Frac { num, den, .. } = &n[1] else { panic!("{n:#?}") };
|
||
assert_eq!(den, &vec![run("2a")]);
|
||
assert!(num.iter().any(|m| matches!(m, MNode::Rad { .. })), "{num:#?}");
|
||
let MNode::Rad { e, .. } = num.iter().find(|m| matches!(m, MNode::Rad { .. })).unwrap() else { panic!() };
|
||
assert!(matches!(e.first(), Some(MNode::Script { kind: ScriptKind::Sup, .. })), "{e:#?}");
|
||
}
|
||
|
||
#[test]
|
||
fn scripts_and_nary() {
|
||
let n = parse_linear("∑_(i=1)^n▒i^2");
|
||
let MNode::Nary { chr, sub, sup, e, .. } = &n[0] else { panic!("{n:#?}") };
|
||
assert_eq!(*chr, '∑');
|
||
assert_eq!(sub, &vec![run("i=1")]);
|
||
assert_eq!(sup, &vec![run("n")]);
|
||
assert!(matches!(e.first(), Some(MNode::Script { .. })));
|
||
let n = parse_linear("x_i^2");
|
||
assert!(matches!(&n[0], MNode::Script { kind: ScriptKind::SubSup, .. }), "{n:#?}");
|
||
}
|
||
|
||
#[test]
|
||
fn functions_and_matrices() {
|
||
let n = parse_linear("sin x");
|
||
assert!(matches!(&n[0], MNode::Func { .. }), "{n:#?}");
|
||
let n = parse_linear("■(a&b@c&d)");
|
||
let MNode::Matrix { rows, .. } = &n[0] else { panic!("{n:#?}") };
|
||
assert_eq!(rows.len(), 2);
|
||
assert_eq!(rows[0].len(), 2);
|
||
}
|
||
|
||
#[test]
|
||
fn linear_round_trip_keeps_structure() {
|
||
for s in [
|
||
"x=(-b±√(b^2-4ac))/2a",
|
||
"∑_(i=1)^n▒i",
|
||
"a/b+c",
|
||
"E=mc^2",
|
||
"√(3&x)",
|
||
"├]a[┤",
|
||
"{█(x@y)┤",
|
||
"|x|+‖v‖",
|
||
"⏞(a+b)┴k",
|
||
"_1^n▒Y",
|
||
"sin^(−1)x",
|
||
"lim┬(n→∞)a_n",
|
||
"A⃗+x̂",
|
||
"▭(a)+¯(b)+▁(c)",
|
||
"(a│b)",
|
||
"E=mc^2#(1)",
|
||
] {
|
||
let n = parse_linear(s);
|
||
let back = parse_linear(&to_linear(&n));
|
||
assert_eq!(n, back, "{s} → {}", to_linear(&n));
|
||
}
|
||
}
|
||
|
||
//T1
|
||
/// Deepest nesting of `a` (a leaf counts 1), without recursion.
|
||
fn depth_of(a: &[MNode]) -> usize {
|
||
let mut best = 0;
|
||
let mut stack: Vec<(&MNode, usize)> = a.iter().map(|n| (n, 1)).collect();
|
||
while let Some((n, d)) = stack.pop() {
|
||
best = best.max(d);
|
||
each_arg(n, &mut |a| stack.extend(a.iter().map(|c| (c, d + 1))));
|
||
}
|
||
best
|
||
}
|
||
|
||
/// Run `f` on a thread with a stack far below the 8 MB of a main thread (#1456).
|
||
fn on_small_stack(f: impl FnOnce() + Send + 'static) {
|
||
std::thread::Builder::new().stack_size(512 * 1024).spawn(f).unwrap().join().unwrap();
|
||
}
|
||
|
||
#[test]
|
||
fn deeply_chained_input_stays_shallow() {
|
||
on_small_stack(|| {
|
||
let cases: Vec<(&str, Arg)> = vec![
|
||
("x^1^1…", parse_linear(&format!("x{}", "^1".repeat(9999)))),
|
||
("a/a/a…", parse_linear(&format!("a{}", "/a".repeat(9999)))),
|
||
("accents", parse_linear(&format!("x{}", "\u{302}".repeat(9999)))),
|
||
("limits", parse_linear(&format!("x{}", "┬a".repeat(9000)))),
|
||
("(a b)^1^1…", parse_linear(&format!("(a b){}", "^1".repeat(9000)))),
|
||
("latex x^1^1…", crate::math_latex::parse_latex(&format!("x{}", "^1".repeat(9999)))),
|
||
("latex \\sum…", crate::math_latex::parse_latex(&"\\sum".repeat(5000))),
|
||
("latex \\sin x^1…", crate::math_latex::parse_latex(&format!("\\sin x{}", "^1".repeat(9000)))),
|
||
];
|
||
for (name, n) in cases {
|
||
assert!(!n.is_empty(), "{name}");
|
||
assert!(depth_of(&n) <= 70, "{name}: depth {}", depth_of(&n));
|
||
let copy = n.clone();
|
||
assert_eq!(copy, n, "{name}");
|
||
let _ = to_linear(&n);
|
||
let _ = crate::math_latex::to_latex(&n);
|
||
let json = serde_json::to_string(&n).unwrap();
|
||
let back: Arg = serde_json::from_str(&json).unwrap();
|
||
assert_eq!(back, n, "{name}");
|
||
}
|
||
});
|
||
}
|
||
|
||
#[test]
|
||
fn ordinary_nesting_is_still_built() {
|
||
// Well below the cap: scripts, fractions and operators still wrap.
|
||
let n = parse_linear(&format!("x{}", "^1".repeat(10)));
|
||
assert_eq!(depth_of(&n), 11, "{n:#?}");
|
||
let n = crate::math_latex::parse_latex(r"\sum_{i}\sum_{j}a_{ij}");
|
||
assert!(matches!(&n[0], MNode::Nary { e, .. } if matches!(e.first(), Some(MNode::Nary { .. }))), "{n:#?}");
|
||
}
|
||
|
||
//T2
|
||
#[test]
|
||
fn latex_text_escapes_what_latex_reads_as_markup() {
|
||
for text in ["a}b\\c", "{x}", "50% of #1", "a_b&c$d~e^f", "\\", "\\alpha", "\\{"] {
|
||
let n = vec![MNode::Run(MRun { text: text.into(), nor: true, sty: Some(MSty::Plain), ..Default::default() })];
|
||
let tex = crate::math_latex::to_latex(&n);
|
||
assert_eq!(crate::math_latex::parse_latex(&tex), n, "{text:?} → {tex}");
|
||
}
|
||
let n = vec![MNode::Run(MRun::new("a\\b"))];
|
||
assert_eq!(crate::math_latex::parse_latex(&crate::math_latex::to_latex(&n)), n);
|
||
}
|
||
|
||
//T3
|
||
#[test]
|
||
fn latex_runs_merge_inside_every_structure() {
|
||
use crate::math_latex::parse_latex;
|
||
for (tex, lin) in [(r"\overline{ab}", "¯(ab)"), (r"\underline{ab}", "▁(ab)"), (r"\boxed{ab}", "▭(ab)"), (r"\phantom{ab}", "⟡(ab)")] {
|
||
assert_eq!(parse_latex(tex), parse_linear(lin), "{tex}");
|
||
}
|
||
let n = parse_latex(r"\begin{matrix}a b&c d\\e f&g\end{matrix}");
|
||
let MNode::Matrix { rows, .. } = &n[0] else { panic!("{n:#?}") };
|
||
assert!(rows.iter().flatten().all(|c| c.len() == 1), "{rows:#?}");
|
||
let n = parse_latex(r"\hat{ab}\underbrace{ab}\underset{ab}{cd}");
|
||
let runs = |a: &Arg| a.iter().filter(|n| matches!(n, MNode::Run(_))).count();
|
||
assert!(matches!(&n[0], MNode::Acc { e, .. } if runs(e) == 1), "{n:#?}");
|
||
assert!(matches!(&n[1], MNode::GroupChr { e, .. } if runs(e) == 1), "{n:#?}");
|
||
assert!(matches!(&n[2], MNode::Lim { e, lim, .. } if runs(e) == 1 && runs(lim) == 1), "{n:#?}");
|
||
}
|
||
|
||
#[test]
|
||
fn multi_letter_scripts_round_trip() {
|
||
// A script reads one letter or a number, so `V_dd` is V_d then d: longer scripts are grouped.
|
||
let script = |kind, sub: &str, sup: &str| MNode::Script { kind, base: vec![run("V")], sub: parse_linear(sub), sup: parse_linear(sup) };
|
||
for n in [
|
||
vec![script(ScriptKind::Sub, "dd", "")],
|
||
vec![script(ScriptKind::Sup, "", "ab")],
|
||
vec![script(ScriptKind::SubSup, "in", "2")],
|
||
vec![MNode::Nary {
|
||
chr: '∑',
|
||
lim_loc: None,
|
||
grow: false,
|
||
sub_hide: false,
|
||
sup_hide: false,
|
||
sub: vec![run("ij")],
|
||
sup: vec![run("n")],
|
||
e: vec![run("x")],
|
||
}],
|
||
vec![MNode::Lim { upper: false, e: vec![run("⟶")], lim: vec![run("yields")] }],
|
||
] {
|
||
assert_eq!(parse_linear(&to_linear(&n)), n, "{}", to_linear(&n));
|
||
}
|
||
// Numbers and single letters stay bare.
|
||
assert_eq!(to_linear(&[script(ScriptKind::SubSup, "10", "2.5")]), "V_10^2.5");
|
||
assert_eq!(to_linear(&[script(ScriptKind::Sub, "d", "")]), "V_d");
|
||
}
|
||
|
||
#[test]
|
||
fn hostile_linear_never_panics() {
|
||
for s in ["", "/", "^", "_", "√", "∑", "((((", "))))", "■(", "█(@@&&", "a/", "/b", "^^^__", "√(&)", "∫_^▒", "lim_", "sin"] {
|
||
let _ = to_linear(&parse_linear(s));
|
||
}
|
||
let deep = "(".repeat(5000) + &")".repeat(5000);
|
||
let _ = parse_linear(&deep);
|
||
let deep = "√".repeat(3000);
|
||
let _ = parse_linear(&deep);
|
||
}
|
||
}
|